Proportional hazards tests and diagnostics based on weighted residuals
1994/01/01 by PATRICIA M. GRAMBSCH, Patricia M. Grambsch, Terry M. Therneau +1 · 78 citations
Mathematics · #Advanced Statistical Methods and Models #Advanced Causal Inference Techniques #Statistical Methods and Inference
paper · doi:10.1093/biomet/81.3.515
Abstract
SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp fl(t)Zi(t). A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.
Cited by
- Minimal relapse risk and early normalization of survival for patients with Burkitt lymphoma treated with intensive immunochemotherapy: an international study of 264 real‐world patients
- FLCRM: Functional Linear Cox Regression Model
- The Political Dynamics of Portfolio Design in European Democracies
- Plant-Based Dietary Patterns and Risk of Alzheimer Disease and Related Dementias in the Multiethnic Cohort Study
- Rationale, Design, and Experiences from the Vanguard Phase of the Bariatric Surgery for the Reduction of Cardiovascular Events (BRAVE) Trial
- A Gene-Expression Signature as a Predictor of Survival in Breast Cancer
- Ultraprocessed food intake and postmenopausal breast cancer risk in the NIH-AARP Diet and Health Study
- Association Between the Combined Effects of Physical Activity Intensity and Particulate Matter and All-Cause Mortality in Older Adults
- Ten‐year clinical outcomes after drug‐eluting stents implantation according to clinical presentation—Insights from the DECADE cooperation
- Can’t Boil, Won’t Boil: Material Inequality, Information, and Disease Avoidance during a Typhoid Epidemic in Tampere, Finland, in 1916
- Calcium Density of Coronary Artery Plaque and Risk of Incident Cardiovascular Events
- Survival analysis under non-proportional hazards: investigating non-inferiority or equivalence in time-to-event data
- Modeling Long-term Outcomes and Treatment Effects After Androgen Deprivation Therapy for Prostate Cancer
- CARTOONS KILL: casualties in animated recreational theater in an objective observational new study of kids' introduction to loss of life
- Evolution on the Shoulders of Giants: Entrepreneurship and Firm Survival in the German Laser Industry
- Determinants of CD19-positive vs CD19-negative relapse after tisagenlecleucel for B-cell acute lymphoblastic leukemia
- Bayesian models for survival data of clinical trials: Comparison of implementations using R software
- The Determinants of Survival of Spanish Manufacturing Firms
- Tumor-Infiltrating Neutrophils after Neoadjuvant Therapy are Associated with Poor Prognosis in Esophageal Cancer
- Joint Modelling of Goals and Bookings in Association Football
- Using fractional polynomials and restricted cubic splines to model non‐proportional hazards or time‐varying covariate effects in the Cox regression model
- Association between trajectories of buprenorphine treatment and emergency department and in‐patient utilization
- Understanding movement and habitat‐use to guide reintroductions and habitat rehabilitation for a nonmigratory freshwater fish
- Mate-switching is not associated with offspring fitness in a socially monogamous bird
- Causes and consequences of divorce in a long‐lived socially monogamous bird
- Elucidating acquired PARP inhibitor resistance in advanced prostate cancer
- Ruxolitinib-induced reactivation of cytomegalovirus and Epstein-Barr virus in graft-versus-host disease
- The Shared Weighted Lindley Frailty Model for Clustered Failure Time Data
- Associations between demographic, clinical and dietary factors and flares in inflammatory bowel disease: the PRognostic effect of Environmental factors in Crohn’s and Colitis (PREdiCCt) prospective cohort study
- Gender Bias in Medieval Inquisitions and its Place in Shaping Knowledge about the Heterodox
- Studentized Permutation Method for Comparing Restricted Mean Survival Times with Small Sample from Randomized Trials
- First-Line Systemic Treatment for Initially Unresectable Colorectal Liver Metastases
- The Role of Social Feedback in Financing of Technology Ventures
- Associations of plant-based diets with all-cause and cause-specific mortality and life expectancy among participants with cardiometabolic disorders from UK, USA, and China
- Persistent and emerging cancer risks after migration: Evidence from North and South Korean cohorts
- A naturally occurring mitochondrial genome variant confers broad protection from infection in Drosophila
- Comparative analysis of robotic, laparoscopic, and open ileal pouch–anal anastomosis outcomes: retrospective cohort study
- Respiratory viral infections awaken metastatic breast cancer cells in lungs
- Stool-Based Molecular Tuberculosis Treatment Monitoring: A Faster Means for Detecting Persistent Mycobacteria Compared to Phenotypic Culture
- New‐onset autoimmune disease following SARS‐CoV‐2 infection and mRNA vaccination in Norway: A retrospective cohort study
- Use of the concordance index for predictors of censored survival data
- Mediation analysis for mixture Cox proportional hazards cure models
- Long-term implant survival in delayed breast reconstruction
- Time-To-Employment and Labor Market Integration of Young Statistics Graduates in Algeria: A Duration Model Approach
- Techniques to predict survival outcomes in nephrology: basics and traditional methods
- Prenatal exposure to per- and polyfluoroalkyl substances (PFAS) and incidence of asthma and wheeze in childhood: A register-based cohort study in Ronneby, Sweden
- ADHAM: Additive Deep Hazard Analysis Mixtures for Interpretable Survival Regression
- On the implications of proportional hazards assumptions for competing risks modelling
- Association between healthy plant-based diet-lifestyle (hPDI-Lifestyle) score and incidence of coronary heart disease, and effect modification by genetic predisposition: a prospective analysis in a population-based cohort
- Multiple adverse outcomes associated with antipsychotic use in people with dementia: population based matched cohort study
- Beyond binary classification of non-proportional hazards: Methodological considerations for interpreting pivotal HCC trials
- Economic Crisis and Democratic Breakdown in the Interwar Years: A Reassessment
- Each additional hour of cold ischemia time significantly increases the risk of graft failure and mortality following renal transplantation
- TP53 mutation status and gene expression profiles are powerful prognostic markers of breast cancer. [europepmc]
- Effect of dexmedetomidine versus lorazepam on outcome in patients with sepsis: an a priori-designed analysis of the MENDS randomized controlled trial. [europepmc]
- Variables with time-varying effects and the Cox model: some statistical concepts illustrated with a prognostic factor study in breast cancer. [europepmc]
- Ki67, chemotherapy response, and prognosis in breast cancer patients receiving neoadjuvant treatment. [europepmc]
- Association between exposure to low to moderate arsenic levels and incident cardiovascular disease. A prospective cohort study. [europepmc]
- Calcium density of coronary artery plaque and risk of incident cardiovascular events. [europepmc]
- The familial risk of autism. [europepmc]
- No evidence that frailty modifies the positive impact of antihypertensive treatment in very elderly people: an investigation of the impact of frailty upon treatment effect in the HYpertension in the Very Elderly Trial (HYVET) study, a double-blind, placebo-controlled study of antihypertensives in people with hypertension aged 80 and over. [europepmc]
- Development and Validation of a Clinically Based Risk Calculator for the Transdiagnostic Prediction of Psychosis. [europepmc]
- Time-dependent ROC curve analysis in medical research: current methods and applications. [europepmc]
- Association Between Inherited Germline Mutations in Cancer Predisposition Genes and Risk of Pancreatic Cancer. [europepmc]
- Time-varying covariates and coefficients in Cox regression models. [europepmc]
- Effect of High-Flow Nasal Oxygen vs Standard Oxygen on 28-Day Mortality in Immunocompromised Patients With Acute Respiratory Failure: The HIGH Randomized Clinical Trial. [europepmc]
- Association of Blood Pressure Classification in Young Adults Using the 2017 American College of Cardiology/American Heart Association Blood Pressure Guideline With Cardiovascular Events Later in Life. [europepmc]
- Effect of Intensive vs Standard Blood Pressure Control on Probable Dementia: A Randomized Clinical Trial. [europepmc]
- Effect of a Resuscitation Strategy Targeting Peripheral Perfusion Status vs Serum Lactate Levels on 28-Day Mortality Among Patients With Septic Shock: The ANDROMEDA-SHOCK Randomized Clinical Trial. [europepmc]
- Association of HIV Preexposure Prophylaxis With Incidence of Sexually Transmitted Infections Among Individuals at High Risk of HIV Infection. [europepmc]
- Association of Metabolic Surgery With Major Adverse Cardiovascular Outcomes in Patients With Type 2 Diabetes and Obesity. [europepmc]
- Patient-Reported Outcomes Through 5 Years for Active Surveillance, Surgery, Brachytherapy, or External Beam Radiation With or Without Androgen Deprivation Therapy for Localized Prostate Cancer. [europepmc]
- Clinical characteristics and day-90 outcomes of 4244 critically ill adults with COVID-19: a prospective cohort study. [europepmc]
- Effect of Postreinduction Therapy Consolidation With Blinatumomab vs Chemotherapy on Disease-Free Survival in Children, Adolescents, and Young Adults With First Relapse of B-Cell Acute Lymphoblastic Leukemia: A Randomized Clinical Trial. [europepmc]
- Effect of Camrelizumab vs Placebo Added to Chemotherapy on Survival and Progression-Free Survival in Patients With Advanced or Metastatic Esophageal Squamous Cell Carcinoma: The ESCORT-1st Randomized Clinical Trial. [europepmc]
- Effect of High-Flow Oxygen Therapy vs Conventional Oxygen Therapy on Invasive Mechanical Ventilation and Clinical Recovery in Patients With Severe COVID-19: A Randomized Clinical Trial. [europepmc]
- Association of Bariatric Surgery With Cancer Risk and Mortality in Adults With Obesity. [europepmc]
- Panitumumab vs Bevacizumab Added to Standard First-line Chemotherapy and Overall Survival Among Patients With RAS Wild-type, Left-Sided Metastatic Colorectal Cancer: A Randomized Clinical Trial. [europepmc]
Related